Hopf Bifurcation of a generalized Moon-Rand system

Agraïments: The second author is supported by Portuguese National Funds through FCT - Fundação para a Ciência e a Tecnologia within the project PTDC/MAT/117106/2010 and by PEst-OE/EEI/LA0009/2013 (CAMGSD).We study the Hopf bifurcation from the equilibrium point at the origin of a generalized Moon-Rand system. We prove that the Hopf bifurcation can produce 8 limit cycles. The main tool for proving these results is the averaging theory of fourth order. The computations are not difficult, but very big and have been done with the help of Mathematica and Mapple